To solve the equation, we need to let u = x²
What is a quadratic equation?A quadratic equation is an algebraic expression that takes the power of the second degree.
From the given parameter:
x⁴ - 17x² + 16 = 0For us to be able to solve the given equation, we need to reduce the equation to a quadratic form.
This can be achieved by making an assumption that:
u = x²So, we will replace x² with u in the given equation.
By doing so, we have:
u² - 17u + 16 = 0Learn more about quadratic equations here:
https://brainly.com/question/1214333
Answer: Solve x4 – 17x2 + 16 = 0.Let u = xX 17x²✔ x²X -17x².
let u = x^2
Step-by-step explanation: just did it
what is the range of the function: h(x)=x+1/x^2 - 7x+10
Answer:
(-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)
Step-by-step explanation:
To make it easier to differentiate, we'll rewrite the function as ...
h(x) = 2/(x-5) -1/(x-2)
Then the derivative is ...
h'(x) = -2/(x-5)^2 +1/(x-2)^2
This will be zero when ...
-2(x-2)^2 +(x-5)^2 = 0
-2(x^2 -4x +4) +(x^2 -10x +25) = 0
-x^2 -2x +17 = 0
x^2 +2x +1 = 17 +1
x +1 = ±√18 = ±3√2
x = -1 ±3√2
The values of the function at these locations are ...
h(-1-3√2) = -1 +(2/3)√2 ≈ -1.9428
h(-1+3√2) = -1 -(2/3)√2 ≈ -0.0572
Then the range of h(x) is ...
(-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)
Maria and Jose have a large tomato garden. On day 111 when the tomatoes first ripened, they picked 333 tomatoes. Each day thereafter, as more tomatoes ripened, they doubled the number of tomatoes they picked. Let T be the number of tomatoes picked on day d. Which of the following best explains the relationship between d and T?
Answer:
T = 3(2)ᵈ⁻¹
Step-by-step explanation:
This is a geometric series, where the first term is 3 and the common ratio is 2.
T = 3(2)ᵈ⁻¹
This can be rewritten as:
T = ³/₂ (2)ᵈ
A kilobyte is 2*10 bytes and a megabyte is 2*20 bytes. How many kilobytes are in a megabyte?
Answer:
10KB = 1MB
Step-by-step explanation:
Since 1KB => 2*10bytes
1MB => 2*20bytes
Therefore 10KB => 1MB
.....................
Answer:
B. √16 × √6
C. √96
Step-by-step explanation:
4√6
4 can be written as a square root.
4 = √16
√16 × √6
The square roots are multiplied, they can be written under one whole square root.
√(16 × 6)
√96
look at pic to see question
Answer:
1/2*base*height
Step-by-step explanation:
All triangles have the area of 1/2*base* height.
Answer:
1/2 * b * h
Step-by-step explanation:
Does the problem involve permutations or combinations? Do not solve. From 8 names on a ballot, a committee of 5 will be elected to attend a political national convention. How many different committees are possible?
Answer: Combination
There are 56 committees possible
============================================
Explanation:
The reason why we know we'll use a combination (instead of a permutation) is because order does not matter. There are no ranking positions on a committee. No one person has a special job compared to the other. The ordering of a committee doesn't matter. All that matters is the entire group itself. For instance, if we had people A,B,C then the committee ABC is the same as CBA and BAC. We would have to introduce a different person, say person D, to get a new committee group.
We have n = 8 people overall to choose from and r = 5 slots to fill. Use the combination formula to get
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_8 C _5 = \frac{8!}{5!*(8-5)!}\\\\_8 C _5 = \frac{8!}{5!*3!}\\\\_8 C _5 = \frac{8*7*6*5!}{5!*3!}\\\\_8 C _5 = \frac{8*7*6}{3!}\\\\_8 C _5 = \frac{8*7*6}{3*2*1}\\\\_8 C _5 = \frac{56*6}{6}\\\\_8 C _5 = 56\\\\[/tex]
We can conclude there are 56 different committees possible.
1
If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term
If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].
We're given
[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]
So the first five terms in the GP are
3, 6, 12, 24, 48
Adding up the first four gives a sum of 45.
If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:
[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]
Multiply both sides by 2:
[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]
Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:
[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]
Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].
Decide which chi-square test (goodness-of fit, homogeneity, or independence) would be most appropriate for the given situation.
A car insurance company performed a study to determine whether an association exists between age and the frequency of car accidents. They obtained the following sample data.
Age Group
Under 25 25-45 Over 45 Total
Number of accidents in past 3 years 0 74 90 84 248
1 19 8 12 39
1 7 2 4 13
Total 100 100 100 300
A. Test for Homogeneity.
B. Test for Independence.
C. Test for Goodness-of-fit.
Answer:
C. Test for Goodness-of-fit.
Step-by-step explanation:
C. Test for Goodness-of-fit would be most appropriate for the given situation.
A. Test Of Homogeneity.
The value of q is large when the sample variances differ greatly and is zero when all variances are zero . Sample variances do not differ greatly in the given question.
B. Test for Independence.
The chi square is used to test the hypothesis about the independence of two variables each of which is classified into number of attributes. They are not classified into attributes.
C. Test for Goodness-of-fit.
The chi square test is applicable when the cell probabilities depend upon unknown parameters provided that the unknown parameters are replaced with their estimates and provided that one degree of freedom is deducted for each parameter estimated.
pls any one it's urgent
Answer:
1. x = 36 is the answer.2. x = 123 is the answer.Step-by-step explanation:
1. 4x = angle 4
x = angle 1
Angle 1 + angle 4 = 180
4x + x = 180
5x = 180
x = 36.2. 55 = angle 2
angle 1 = 68
angle 3 = 55 + 68 = 123 = 180 - 123 = 57
Angle 4 = 57
180 - 57 = 123x = 123Hope this helped,
kavitha
Susan purchased 9/10 of a pound of shrimp for a dinner party. Her plan is to serve 1/6 of a pound of shrimp to herself and each guest. Including herself, how many people can Susan serve at her dinner party? (Remember that you can't have a fraction of a person.)
Answer:
Susan and 4 quests
5 people
Step-by-step explanation:
Take 9/10 and divide by 1/6
9/10 ÷1/6
Copy dot flip
9/10 * 6/1
54/10
50/10 + 4/10
5 4/10
We can only serve whole numbers
5 people
Susan and 4 quests
WILL MARK BRAINLIEST
PLEASE HELP
Please help me answer 1 and 2 and explain how you did it so I can understand x
Answer:
poop
Step-by-step explanation:
please help !!!!!!!!
Answer:
x=3 y=11
Step-by-step explanation:
2x+3=9
2x=6
x=3
y-4=7
y=11
Please answer this in two minutes
Answer:
54
Step-by-step explanation:
im not that good so u should cheek it first
Answer: 9a + 249
Step-by-step explanation: 9a + 249 and a would be one cause these numbers are independent
2. The volume of the cylinder correct to 3 significant figures is"
Calculate the volume of the cylinder with a diameter of 10
meters and a height of 8 meters.
Answer:
628 meters²Option D is the correct option.
Step-by-step explanation:
Given,
Diameter ( D ) = 10 meters
Radius ( r ) = 10 ÷ 2 = 5 meters
Height ( h ) = 8 meters
Volume = ?
Now, let's find the volume of the given cylinder:
[tex]\pi \: {r}^{2} h[/tex]
Plug the values
[tex] = 3.14 \times {5}^{2} \times 8[/tex]
Evaluate the power
[tex] = 3.14 \times 25 \times 8[/tex]
Calculate the products
[tex] = 628 \: {m}^{2} [/tex]
Hope this helps...
Best regards!!
what is the vertex of g(x)=3x^2-12x+7? a) (-6,-5) b) (-2,-5) c) (2,-5) d) (6,-5)
Step-by-step explanation:
Answer:
The answer is C.) (2, -5)
lily wants to buy a new smartphone. she has $500 to spend. list three way she can get good deal
by bargaining with the owner, vying for discounts or insisting on multiple products for a complimentary value deal
which platonic solid has eight faces that are equilateral triangles? A, dodecahedron, B, octahedro, C, tetrahedron, D, icosahedron
Answer:
Octahedron Answer B) in your list
Step-by-step explanation:
The octahedron is the three dimensional figure that contains 8 equilateral triangles as its faces. It looks like 2 pyramids with square base and lateral equilateral triangles joined by their square bases
Answer:
C
Step-by-step explanation:
apeeeex
PLEASE HELP ME GUYS!! Write and solve equations based on the angle relationships in the diagram below to find the measure of ∠EKC and ∠CKA
Answer:
x = 65°
y = 25° (equations in explanation)
Step-by-step explanation:
We know that EKD is 25° and we know that DKB is 90°.
EKD, DKB, and BKF are supplementary. This means that their angle measures add up to 180°.
So, since we know two, we can find the other very easily.
[tex]180 - (25+90)\\180 - 115\\65[/tex]
This means that BKF is 65°.
Now, BKF and EKC are alternate interior angles, so they have the exact same measurement. Therefore, EKC, x, is 65°.
Again, EKC, CKA, and AKF are supplementary. AKF is 90° and EKC is 65°, so we can find the measure of CKA easily.
[tex]180 - (65+90)\\180-155\\25[/tex]
Therefore y is 25° and x is 65°.
Hope this helped!
WILL MARK BRAINLIEST! Match each pair of angles with the correct angle relationship(s). Explain your reasoning for each.
Answer:
∠AOB and ∠COD are vertical angles
∠DOE and ∠COD are complementary, adjacent
∠AOB and ∠AOD are supplementary, adjacent.
Step-by-step explanation:
Let's start with ∠AOB and ∠COD.
Looking at this, we can see they are the same angles formed by two lines that intersected. These are vertical angles as they are opposite each other.
∠DOE and ∠COD together form the angle ∠EOC, which is a right angle. Complementary angles are any of two that add up to 90°, so these two angles are complementary. They are also adjacent because they are right next to each other.
∠AOB and ∠AOD together form the angle ∠BOD, which has a measure of 180°. Supplementary angles are any of two that add up to 180°, so ∠AOB and ∠AOD are supplementary. They are also adjacent as they are touching/right next to each other.
I hope this helped!
The coefficient of x^ky^n-k in the expansion of (x+y)^n equals (nk). True or false.
Answer:
The correct option is;
False
Step-by-step explanation:
The coefficient of x^k·y^(n-k) is nk, False
The kth coefficient of the binomial expansion, (x + y)ⁿ is [tex]\dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)[/tex]
Where;
k = r - 1
r = The term in the series
For an example the expansion of (x + y)⁵, we have;
(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵
The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15
Therefore, the coefficient of x^k·y^(n-k) for the expansion (x + y)ⁿ = [tex]C(n,k)[/tex] not nk
Answer:
True
Step-by-step explanation:
apec
Place these numbers in correct order and and simplify 25x^2 +6x^3 -7 +17 -24x^4 +6
Answer:
[tex]-24x^4+6x^3+25x^2+16[/tex]
Step 1:
We need to place the numbers in descending order of the power. Here, [tex]-24x^4[/tex] has the largest power, so that number goes first. We keep doing this until we end up with our final expression, placed in order based on the powers.
[tex]-24x^4+6x^3+25x^2+17-7+6[/tex]
Step 2:
We can see that the last three numbers, 17, -7, and 6, don't have variables or powers, so we simplify by adding (and subtracting) them.
[tex]17-7=10\\10+6=16[/tex]
Our final equation:
[tex]-24x^4+6x^3+25x^2+16[/tex]
Instructions: Find the missing length indicated.
I
Answer:
x = 12 units
Step-by-step explanation:
In the picture attached,
Since, DE and BC are the parallel lines,AC and AB are the transverse.
Therefore, ∠AED ≅ ∠ABC [Alternate angles]
∠ADE ≅ ∠ACB [Alternate angles]
ΔADE ~ ΔACB [By AA postulate of similarity]
By the property of similarity,
If two triangles are similar then their corresponding sides will be proportional.
[tex]\frac{\text{AB}}{\text{AE}}=\frac{\text{AC}}{\text{AD}}[/tex]
[tex]\frac{(4+8)}{4}=\frac{(6+x)}{6}[/tex]
[tex]3=1+\frac{x}{6}[/tex]
x = 12
Therefore, length of missing segment is 12 units.
Can someone plz answer the question ASAP? Thank you. multiple choice answer yes or no
Answer:yes
Step-by-step explanation:
$70 discounted to $63
Answer:
10% off
Step-by-step explanation:
When $70 is discounted to $63, you can multiply 70 times 0.1 to get 7 which 70-63=7. To make 0.1 to a percentage, multiply by 100 to get 10%.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
What is the slope of the line which passes through (−2, 0) and (0, 4)? (5 points) 2 Undefined −2 0
Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Gradient formula :
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]let \: (x1 \: , \: y1) \: be \: ( - 2 \: , \: 0)[/tex]
[tex]let \: (x2 \: , \: y2) \: be \: (0 \: , \: 4)[/tex]
[tex]m = \frac{4 - 0}{0 - ( - 2)} [/tex]
[tex]m = \frac{4}{2} [/tex]
[tex]m = 2[/tex]
Answer:
2
Step-by-step explanation:
The formula you use to find the slope is
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
First, you want to substitute
[tex]\frac{4-0}{0--2}[/tex]
Which simplifies to
[tex]\frac{4-0}{0+2}[/tex]
Because two negatives equal a positive
The next step is to add and subtract
[tex]\frac{4}{2}[/tex]
Which simplifies to
[tex]\frac{2}{1}[/tex]
Which equals
2.
Hope this helped, if you have any questions, feel free to ask.
Have a good day! :)
y=tan(x-30) period and amplitude
Answer:
No amplitude
Period is pi
Step-by-step explanation:
another scale drawing of Jimmy's living room is shown below:
If each 2 cm on the scale drawing equals 8 feet, what are the actual dimensions of the room?
Length = 8 feet, width = 6 feet
Length = 12 feet, width = 8 feet
Length = 18 feet, width = 16 feet
Length = 24 feet, width = 16 feet
Answer:
last option
Step-by-step explanation:
Again, 1 cm represents 8 / 2 = 4 feet so the width is 4 * 4 = 16 and the length is 6 * 4 = 24.
PLEASE HELPPPPPP 65 points
Answer:
x + 2y ≤ 12
x + 2y = 12
Step-by-step explanation:
The teachers can not give more than 12 hours of homework so this is the answer. those are the 2 equations you can use. It under 12 hours or equal to 12 hours.
Answer:
Part A: x + 2y ≤ 12.
Part B: y = -1/2x + 6.
Part C: (0, 0).
Step-by-step explanation:
Part A: The total hours of homework have to be 12 hours, and it has to be either 12 hours or less. So, we have ≤ 12.
They take 1 math course with x hours of homework, so in total, that is 1 * x = x hours of math homework.
They take 2 science courses with y hours of homework, so in total, that is 2 * y = 2y hours of science homework.
The inequality would then be x + 2y ≤ 12.
Part B: x + 2y = 12
2y = -x + 12
y = -1/2x + 6
You can use the Math is Fun: Function Grapher and Calculator to find the graph of the line, shown below.
Part C: Since the inequality uses a ≤ symbol, we know that the shading will be underneath the line. An appropriate point below the line includes (0, 0). We will test out whether it works as a point included in the inequality.
x + 2y ≤ 12
0 + 2 * 0 ≤ 12
0 + 0 ≤ 12
0 ≤ 12
Since this is a true statement, (0, 0) holds true for the inequality.
Hope this helps!
HELP ME ASAP BRAINLIEST UP FOR GRABS
Answer:
52.0 m
Step-by-step explanation:
The triangle formed by the flagpole, the ground and the 30° line is a right triangle, with x as the required length to be found.
Using the tangent ratio
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{30}{x}[/tex] ( multiply both sides by x )
x × tan30° = 30 ( divide both sides by tan30° )
x = [tex]\frac{30}{tan30}[/tex] ≈ 52.0 m
u can look this up here on brainly for an answer source if you want but do the one that has the greatest points... its on google
Answer:
First one is 41
Second one is 87
Step-by-step explanation:
Make the shaded part as a trapezoid which is (3+6)*10/2 you just have to get rid of 2*2. So you get 41 as the answer.
The unshaded part will be 16*8 then subtracts the shaded part which is 41. Then you get the answer 87.